**3. Charge collection efficiency in CdTe-based Ohmic detectors**

possible due to doping by self-compensated donors and the formation of A- or DX-centers, the concentration of which is practically equal to the concentration of acceptors due to the very nature of these centers. (2) In a certain combination of ionization energy and the compensation degree, changes in the temperature dependence of resistivity and/or inversion of the conductivity type of the crystal in the climate-change temperature range may occur that may affect on the operation of the X/γ-ray detector with the Schottky diode. If the donor level located near the middle of the band gap of the Cd0,9Zn0,1Te crystal (*E*<sup>d</sup> = 0.7 eV), to obtain the resistivity *ρ* = 1010 Ω·сm at 300 К (**Figure 2b**), the compensation degree equals to *ξ* = 0.679, and the thermal activation energy of conductivity is close to the half of the Cd0,9Zn0,1Te band gap at 0 K (Δ*E* = 0.84 eV). If *E*<sup>d</sup> = 0.5 eV to ensure *ρ* = 1010 Ω·сm at 300 K, the compensation level should be increased to 0.99979, which leads to a decrease of Δ*E* to 0.65 eV. When *E*<sup>d</sup> = 0.3 eV, the compensation degree should further increase to 0.9999999, making activation energy decreases to 0.47 eV. If *E*d equals to 0.9 eV to ensure *ρ* = 1010 Ω·сm, the compensation degree should be considerably less than 1/2, namely *ξ* = 0.00047. In this case, the thermal activation energy Δ*E* will be 1.04 eV, that is, it becomes "abnormally" high

**Figure 2c** shows the calculated temperature dependences of the Fermi level energy in Cd0,9Zn0,1Te at different compensation degrees of donor (In) with ionization energy *Е*<sup>d</sup> = 0.45 eV, which corresponds to the often observed in these crystals photoluminescence band (~1.08 eV). The position of the Fermi level in the intrinsic Cd0,9Zn0,1Te is shown by dashed line. As seen, the Fermi level is located above the Fermi level in the intrinsic semiconductor at the compensation degree *ξ* = 0.9999 in the whole temperature range, that is, the semiconductor has an n-type of conductivity. At sufficiently higher compensation degree (*ξ* = 0.999999), the Fermi level is located below the Fermi level in the intrinsic Cd0,9Zn0,1Te, that is, the crystal has p-type conductivity [9]. It is also possible the condition when type of conductivity changes in the

**Figure 2.** (a) The dependence of resistivity of Cd0.9Zn0.1Te crystal on the compensation degree *ξ.* (b) Temperature

the same *ρ,* but different thermal activation energies Δ*E*. (c) The temperature dependences of the Fermi level energy Δ*μ*

*/N*d, which provides


dependences of resistivity *ρ* at the different ionization energies *E*d and compensation degree *ξ* = *N*<sup>a</sup>

(*T*) in Cd0.9Zn0.1Te crystal at the different compensation degrees (Δ*μ*<sup>і</sup>

[5, 7, 9].

32 New Trends in Nuclear Science

conductivity).

The operation of CdTe detector in spectrometric mode assumes complete collection of the charge generated by the absorption of high-energy quanta. Since the lifetime of charge carriers in the most perfect CdTe crystals does not exceed several microseconds, it is necessary to apply a rather high voltage to prevent the "capture" of the carriers by deep impurities (defects). At low voltage applied to the CdTe crystal with ohmic contacts, *I-V* characteristic is linear, but at higher bias a superlinear increase in current is always observed [14]. Attention is drawn to the fact that the deviation from linear *I-V* relationships at higher voltage is observed stronger when the temperature decreases (**Figure 3b**, inset). Therefore, we can assume that an additional charge transport mechanism with much weaker temperature dependence comes into play with increasing voltage. This is confirmed by the data in **Figure 3b**, which show the voltage dependences of the difference Δ*I* between the measured current *I* and a linearly extrapolated current *I*<sup>o</sup> (Δ*I = I* – *I*<sup>o</sup> ). As seen, the current excessive over linearly extrapolated current is virtually independent of temperature. A deviation of *I-V* characteristics from linearity due to lowering the barrier at imperfect Ohmic contact should be rejected because such a mechanism leads to an exponentially increase in the current with temperature [15]. The current caused by tunneling transitions of electrons from the Fermi level in the metal (or slightly below it) into the semiconductor can be almost temperature independent [16]. However, at bias voltage in the range 10–100 V, the probability of tunneling is practically zero. A much greater probability of tunneling is through a thin interfacial oxide layer, whose presence on the crystal surface before metal deposition cannot be excluded (**Figure 3c**). At higher voltages, the linear behavior of the *I-V* characteristic of the CdTe crystal is replaced by a quadratic dependence on *V*, as in the case of space charge limited current (SCLC)] according to the Mott-Gurney law [17]. It is confirmed by comparing the experimental data with the extrapolation of the quadratic *I-V* dependence (**Figure 3b**). According to theory, SCLC can be formed by injection of charge carriers into the valence or conduction band. In the case of semi-insulating CdTe, the injection of electrons into the conduction band should be preferred. Firstly, the excess concentration of electrons above the electron equilibrium concentration is achieved much easier, since in the CdTe:Cl crystals the electron concentration approximately two orders of magnitude lower than that of holes. Second, the electron mobility in CdTe is more than an order of magnitude higher than that of holes, and the SCLC is proportional to the charge carrier mobility. Finally, the electron current injected by tunneling is almost temperature independent, that is, observed from the experience and just this one needs to explain. Taking into account the current of thermally generated holes and SCLC we can write:

**Figure 3.** (а) *I-V* characteristics of CdTe crystal measured (circles) and calculated using Eq. (3) at different temperatures (solid lines). The dashed lines show linear extrapolation of *I-V* dependencies at low *V*. (b) Voltage dependence of difference Δ*I* between the measured current *I* and a linearly extrapolated current *I*<sup>o</sup> for three temperatures. The straight solid line extrapolates quadratic dependence of the current on voltage. The inset shows temperature dependences of the currents at 1 and 100 V. (c) Energy diagram of the metal/CdTe contact showing tunneling of electrons through an intermediate oxide film on the CdTe crystal surface.

$$I = \text{sqp}\_{\circ}(T)\,\mu\_{\rho}\frac{V}{d} + \text{sK}\,\frac{9}{8}\frac{\text{\t}\,\text{\t}\,s\_{\circ}\,\mu\_{\text{\t}}}{d^3}V^2\_{\prime} \tag{3}$$

of the crystal and the applied voltages, the recombination on the surfaces of the crystal can be neglected. Neglecting recombination losses at the crystal surfaces, we have to assume that the low efficiency of charge collection in Ohmic-type CdTe detectors is caused by trapping of photogenerated charge carriers by deep levels of impurities (defects) in the crystal bulk. These losses is strongly dependent on the lifetime of charge carriers (*τ*n and *τ*p), which at a given electric field *F* (together with their mobility (*μ*n and *μ*p) determine the drift length of carriers *λ*<sup>n</sup> = *μ*n*Fτ*n, *λ*<sup>p</sup> = *μ*p*Fτ*p. In this view, the relationship between the CdTe crystal thickness and the drift length of carriers (**Figure 4a**, inset) is very important. A quantitative description of the collection losses of photogenerated charge carriers gives the well-known Hecht equation,

Mechanisms of Charge Transport and Photoelectric Conversion in CdTe-Based X- and Gamma-Ray Detectors

which for a uniform electric field has the form [19].

*d* [

0

<sup>1</sup> <sup>−</sup> exp(−\_\_\_\_ *<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*

*<sup>λ</sup><sup>n</sup>* )] <sup>+</sup>

Taking into account the most important processes which determine the spectral distribution of the quantum detection efficiency, in particular, absorption in the bulk of crystal and an electrode material (Pt), the losses caused by trapping of charge carriers in the bulk of crystal, the detection efficiency depending on the absorption coefficient *α*γ in the crystal with Ohmic

where *Т*Pt(*α*γ) takes into account the radiation attenuation after passing through an electrode material; *η*H(*x*) is Hecht function (4); *α*γexp(−*α*γ*x*) is the generation rate of electron–hole pairs

Insufficient absorptive capacity in high spectral range significantly reduces the registration of X/γ-rays but does not affect the processes that take place after photon absorption. Therefore,

**Figure 4.** (a) Temperature dependences of the current at different voltages applied to the CdTe crystal. The inset shows the dependences of the drift length of holes on the thickness of the CdTe crystal at voltage when the same leakage current of 3 × 10−8 A is achieved. (b) Charge collection efficiency spectra for CdTe crystals of different thicknesses at voltages that corresponds to the same current 3 × 10−8 A. (c) Energy resolution in the spectra of different isotopes for the detector

*λ* \_\_*<sup>p</sup> d* [

<sup>1</sup> <sup>−</sup> exp(

−\_\_*<sup>x</sup> λp*)]

*<sup>d</sup> T*Pt(*αγ*) *αγ* exp(−*αγ x*) *ηH*(*x*)dx, (5)

. (4)

http://dx.doi.org/10.5772/intechopen.78504

35

*<sup>η</sup>H*(*x*) <sup>=</sup> *<sup>λ</sup>*\_\_*<sup>n</sup>*

contacts can be written as

per incident photon [16].

thickness of 0.25 mm at voltage of 10.3 V.

*η*(*αγ*) = ∫

where *ε* is the dielectric permittivity of the semiconductor, *ε*<sup>o</sup> is the dielectric constant of vacuum, *μ*n and *μ*p is the mobility of charge carriers, *s* is the area of the contact, *p*<sup>0</sup> is the equilibrium concentration of holes in the crystal, *K* is the coefficient, which takes into account the probability of electron tunneling through the oxide film and reducing the contribution of the SCLC.

Temperature variation leads to a change in current through the crystal, depending on the SCLC contribution. For the best agreement, the calculation results by Eq. (3) with the experimental data we should substitute *К* = 2.3·10−4. As seen, Eq. (3) well reproduces the voltage dependences of the current and its temperature changes in detail (**Figure 3a**). SCLC negatively impacts on the detector performance since it leads to an increase in leakage current, and hence degrades the energy resolution of the detector. Moreover, the contribution of the SCLC increases with decreasing temperature due to increasing the holes mobility (by 5–6% per 10°C) (**Figure 4a**). Such a character of the SCLC does not allow reduce significantly the leakage current by thermoelectrically cooling of the detector as in the case of CdTe detectors with Schottky diode [18].

SCLC is proportional to the squared voltage and is inversely proportional to the crystal thickness *d*; therefore, the relationship between the CdTe crystal thickness *d* and the drift length of carriers *λ*p increases with decreasing *d* (**Figure 4a**, inset), which, in turn, improves the energy resolution of detector. Thus, too low energy resolution of X/γ-rays CdTe-detector with two Ohmic contacts (6–8%) caused by ineffective charge collection. One of the reasons might be the recombination of charge carriers in the bulk and on the front and back surfaces of the crystal. Analysis of the influence of surface recombination can be made on the base of continuity equation (with the corresponding boundary conditions) and taking into account the drift and diffusion components of the current. The calculations show that for the actual thicknesses of the crystal and the applied voltages, the recombination on the surfaces of the crystal can be neglected. Neglecting recombination losses at the crystal surfaces, we have to assume that the low efficiency of charge collection in Ohmic-type CdTe detectors is caused by trapping of photogenerated charge carriers by deep levels of impurities (defects) in the crystal bulk. These losses is strongly dependent on the lifetime of charge carriers (*τ*n and *τ*p), which at a given electric field *F* (together with their mobility (*μ*n and *μ*p) determine the drift length of carriers *λ*<sup>n</sup> = *μ*n*Fτ*n, *λ*<sup>p</sup> = *μ*p*Fτ*p. In this view, the relationship between the CdTe crystal thickness and the drift length of carriers (**Figure 4a**, inset) is very important. A quantitative description of the collection losses of photogenerated charge carriers gives the well-known Hecht equation, which for a uniform electric field has the form [19].

$$\eta\_{li}(\mathbf{x}) = \frac{\lambda\_\ast}{d} \left[ 1 - \exp\left(-\frac{d-\underline{x}}{\lambda\_\ast}\right) \right] + \frac{\lambda\_\ast}{d} \left[ 1 - \exp\left(-\frac{\underline{x}}{\lambda\_\ast}\right) \right]. \tag{4}$$

Taking into account the most important processes which determine the spectral distribution of the quantum detection efficiency, in particular, absorption in the bulk of crystal and an electrode material (Pt), the losses caused by trapping of charge carriers in the bulk of crystal, the detection efficiency depending on the absorption coefficient *α*γ in the crystal with Ohmic contacts can be written as

*I* = sqp*<sup>o</sup>*

intermediate oxide film on the CdTe crystal surface.

the SCLC.

34 New Trends in Nuclear Science

with Schottky diode [18].

(*T*) *μ<sup>p</sup>* \_\_ *V <sup>d</sup>* <sup>+</sup> sK \_\_<sup>9</sup> 8 εε*<sup>o</sup> μ* \_\_\_\_\_*<sup>n</sup> <sup>d</sup>*<sup>3</sup> *<sup>V</sup>*<sup>2</sup>

vacuum, *μ*n and *μ*p is the mobility of charge carriers, *s* is the area of the contact, *p*<sup>0</sup>

equilibrium concentration of holes in the crystal, *K* is the coefficient, which takes into account the probability of electron tunneling through the oxide film and reducing the contribution of

**Figure 3.** (а) *I-V* characteristics of CdTe crystal measured (circles) and calculated using Eq. (3) at different temperatures (solid lines). The dashed lines show linear extrapolation of *I-V* dependencies at low *V*. (b) Voltage dependence of

solid line extrapolates quadratic dependence of the current on voltage. The inset shows temperature dependences of the currents at 1 and 100 V. (c) Energy diagram of the metal/CdTe contact showing tunneling of electrons through an

Temperature variation leads to a change in current through the crystal, depending on the SCLC contribution. For the best agreement, the calculation results by Eq. (3) with the experimental data we should substitute *К* = 2.3·10−4. As seen, Eq. (3) well reproduces the voltage dependences of the current and its temperature changes in detail (**Figure 3a**). SCLC negatively impacts on the detector performance since it leads to an increase in leakage current, and hence degrades the energy resolution of the detector. Moreover, the contribution of the SCLC increases with decreasing temperature due to increasing the holes mobility (by 5–6% per 10°C) (**Figure 4a**). Such a character of the SCLC does not allow reduce significantly the leakage current by thermoelectrically cooling of the detector as in the case of CdTe detectors

SCLC is proportional to the squared voltage and is inversely proportional to the crystal thickness *d*; therefore, the relationship between the CdTe crystal thickness *d* and the drift length of carriers *λ*p increases with decreasing *d* (**Figure 4a**, inset), which, in turn, improves the energy resolution of detector. Thus, too low energy resolution of X/γ-rays CdTe-detector with two Ohmic contacts (6–8%) caused by ineffective charge collection. One of the reasons might be the recombination of charge carriers in the bulk and on the front and back surfaces of the crystal. Analysis of the influence of surface recombination can be made on the base of continuity equation (with the corresponding boundary conditions) and taking into account the drift and diffusion components of the current. The calculations show that for the actual thicknesses

where *ε* is the dielectric permittivity of the semiconductor, *ε*<sup>o</sup>

difference Δ*I* between the measured current *I* and a linearly extrapolated current *I*<sup>o</sup>

, (3)

is the dielectric constant of

for three temperatures. The straight

is the

$$\eta(\mathbf{a}\_{\boldsymbol{\gamma}}) = \int\_{0}^{\boldsymbol{\mu}} T\_{\text{pf}}(\mathbf{a}\_{\boldsymbol{\gamma}}) \, \underset{\boldsymbol{\gamma}}{\text{exp}} \, \exp(\neg \boldsymbol{a}\_{\boldsymbol{\gamma}} \mathbf{x}) \, \eta\_{\boldsymbol{\mu}}(\mathbf{x}) \, \text{d}\mathbf{x},\tag{5}$$

where *Т*Pt(*α*γ) takes into account the radiation attenuation after passing through an electrode material; *η*H(*x*) is Hecht function (4); *α*γexp(−*α*γ*x*) is the generation rate of electron–hole pairs per incident photon [16].

Insufficient absorptive capacity in high spectral range significantly reduces the registration of X/γ-rays but does not affect the processes that take place after photon absorption. Therefore,

**Figure 4.** (a) Temperature dependences of the current at different voltages applied to the CdTe crystal. The inset shows the dependences of the drift length of holes on the thickness of the CdTe crystal at voltage when the same leakage current of 3 × 10−8 A is achieved. (b) Charge collection efficiency spectra for CdTe crystals of different thicknesses at voltages that corresponds to the same current 3 × 10−8 A. (c) Energy resolution in the spectra of different isotopes for the detector thickness of 0.25 mm at voltage of 10.3 V.

the spectral distribution of the charge collection efficiency (the value determining the energy resolution of the detector) is obtained by dividing the detection efficiency *η*(*hν*) by the absorption capacity of the crystal *A*(*hν*) *=* 1 - exp(−*α*γ*d*). **Figure 4b** shows the collection efficiency curves *η*<sup>o</sup> (*hν*) calculated for the different thicknesses of CdTe and voltages at which the current is the same as at voltage of 60 V for crystal thickness of 1 mm (3·10−8 A). As seen, when the crystal thickness is 4 mm, the charge collection efficiency *η*<sup>o</sup> (*hν*) in the photon energy *hν* < 100 keV is 90%, while for *hν* ≈ 1 MeV *η*<sup>o</sup> (*hν*) is reduced to 77% (**Figure 4b**). When the crystal thins, the charge collection efficiency is significantly improved reaching a level of 97–98%. With the thickness of 0.25 mm the charge collection efficiency is above 97% throughout the whole spectral range. However, increasing the charge collection efficiency *η*<sup>o</sup> (*hν*) with thinning of the crystal is achieved with a significant decrease in the efficiency of detection (registration) in the range of high-energy photons. A significant increase in the energy resolution can be achieved by improving the quality of CdTe crystals and, thus, increasing the lifetime of charge carriers. Our calculations show that with increasing the electron lifetime by the order of magnitude from 3 × 10−6 s to 3 × 10−5 s, for the crystal thickness of 0.25 mm at voltage that corresponds to the current 3 × 10−8 A (10.3 V) the energy resolution in the spectra of all isotopes is higher than 99% [20] (**Figure 4c**).

100 V is also quite high Δ*E* = 0.65 eV, which causes its significant growth from temperature. The voltage dependence of the current, surplus of equilibrium current, found by extrapolation of the linear part of the *I-V* characteristic at low voltages has a complex form. In the voltage range *V* = 20–40 V the current is rapidly increasing, at high voltages (up to the highest voltages), the power Δ*I* ~*V* 2,4–2,5 is observed. This behavior of the Au/CdZnTe/Au detector characteristics contradicts the SCLC theory. Therefore, the reason for the deviation of the current from the linear dependence is the injection of minority charge carriers (holes) due to

Mechanisms of Charge Transport and Photoelectric Conversion in CdTe-Based X- and Gamma-Ray Detectors

The section deals with electrical characteristics of Ni/CdTe/Ni X/γ-rays detectors with

The theoretical analysis of experimental results allows identifying and explaining the essential features of the charge transport mechanisms depending on the resistivity of the material and the parameters of the diode structure, in particular the concentration of uncompensated impurities (defects) and the height of the potential barrier on Schottky contact [21]. According to the Sah-Noyce-Shockley theory, the current through the diode is determined by the integration of the generation-recombination rate over the whole space charge region (SCR) width [22].

*<sup>W</sup> <sup>n</sup>*(*x*, *<sup>V</sup>*)*p*(*x*, *<sup>V</sup>*) <sup>−</sup> *ni*

where *А* is the diode area, *q* electron charge, *W* is the width of the SCR, *n*(*x,V*) and *p*(*x,V*) - are the concentrations of charge carriers in the conduction and valence bands, respectively, *τ*no and *τ*po -

. The results of calculations of the *I*–*V* characteristic, by using formula (6) show that the model of generation-recombination processes in the SCR adequately describes not only the current dependence on the voltage, but also the temperature induced variations in the Ni/p-CdTe Schottky diode *I*–*V* characteristic: (1) The reverse current, which has a generation origin, cannot vary in a wide range of the material resistivity *ρ* since this current is governed by the carrier lifetime and by the thickness of the SCR, which have no direct relation with a value of *ρ*. (2) In the region of low forward biases, where the dependence *I* ∝ exp(*qV*/2*kT*) – 1 holds, the current is governed by the same parameters and, therefore, is also only slightly *ρ*-dependent. (3) As *ρ* increases, the Fermi level recedes from the valence band; that is, *∆μ* increases at the same time

 decreases. In this case, the part of the forward branch, where the forward current is proportional to exp(*qV*/2*kT*), is increasingly restricted from above, as is observed in the experimental

are the effective lifetimes of electrons and holes in the SCR, and the quantities *n*<sup>1</sup> = *N*<sup>c</sup>

\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ *<sup>τ</sup>*po[*n*(*x*, *<sup>V</sup>*) <sup>+</sup> *<sup>n</sup>*1] <sup>+</sup> *<sup>τ</sup>*no[*p*(*x*, *<sup>V</sup>*) <sup>+</sup> *<sup>p</sup>*1]

2

)/*kT*] are determined by the depth of the generation-recombination level

dx, (6)

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37

exp(−*E*<sup>t</sup>

/*kT*)

Schottky diodes based on high-resistivity CdTe single crystals (*ρ* ~109 Ω·сm (300 К)).

**4. Electrical characteristics of Schottky diodes based on semi-**

*<sup>g</sup>*−*<sup>r</sup>* = *Aq* ∫

0

the imperfection of Ohmic contacts.

**insulating CdTe single crystals**

*I*

exp[−(*E*<sup>g</sup>


and *p*<sup>1</sup> = *N*<sup>v</sup>

*E*t

as *φ*<sup>0</sup>

curves.

CdZnTe and CdMnTe-based X/γ-rays Ohmic detectors can have electrical characteristics both similar to presented above and different. This is largely due to the choice of contacts material, the treatment of the crystal surface before contacts fabrication, conditions of post-deposition treatment. At low voltage applied to the p-Cd1-xMn<sup>x</sup> Te (*x* = 0.3) crystal *I-V* characteristics are linear, but at higher bias a superlinear increase in current is observed approximately the same extent at different temperatures. The fact that the voltage dependence of difference between the measured current and a linearly extrapolated current is quadratic, which indicates that the observed supernular growth of current is due to by space charge limited current (SCLC) according to the Mott-Gurney law [17]. The activation energy of the conductivity caused by the equilibrium holes (at *V* = 10 V) equals to 0.39 еV. Attention is drawn to the fact that the energy of acceptor trap at the formation of the SCLC in the Ni/CdMnTe contact (at *V* > 200 V), equal also 0.39 еV, that is, impurity (or defect), responsible for electrical conductivity of material and trap of injected charge carriers clearly have the same nature. Therefore, the same activation energy for the current of equilibrium holes and the current surplus of equilibrium current confirms the fact that SCLC in the Ni/CdMnTe/Ni detector is formed by the injection of majority carriers (holes) from the metal, not by the tunnel injection of minority carriers (electrons) as in the case of Pt/CdTe/Pt detectors discussed above.

Cd1-xZn<sup>x</sup> Te (*x* = 0.1) n-type crystals with gold Ohmic contacts show other features of superlinear current growth at high voltages. At voltages, lower ~ 10 V *I-V* characteristic are linear, but at higher bias, the superlinear increase is observed. However, the voltage of deviation from the linear law is 10–20 V regardless of temperature. It turns out that the current of equilibrium electrons and the excess current in the Au/CdZnTe/Au detector are growing approximately equally with the temperature. This is confirmed by the fact that the thermal activation energy of the crystal Cd0,9Zn0,1Te is 0.74 eV, and the thermal activation energy of the excess current at 100 V is also quite high Δ*E* = 0.65 eV, which causes its significant growth from temperature. The voltage dependence of the current, surplus of equilibrium current, found by extrapolation of the linear part of the *I-V* characteristic at low voltages has a complex form. In the voltage range *V* = 20–40 V the current is rapidly increasing, at high voltages (up to the highest voltages), the power Δ*I* ~*V* 2,4–2,5 is observed. This behavior of the Au/CdZnTe/Au detector characteristics contradicts the SCLC theory. Therefore, the reason for the deviation of the current from the linear dependence is the injection of minority charge carriers (holes) due to the imperfection of Ohmic contacts.
